{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "134e7f9d",
   "metadata": {},
   "source": [
    "# Demo 5: Initialization Hyperparamters"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6581dacd",
   "metadata": {},
   "source": [
    "Initialization is the first step to gaurantee good training. Each activation function is initialized to be $\\phi(x)={\\rm scale\\_base}*b(x) + {\\rm scale\\_sp}*{\\rm spline}(x)$.\n",
    "1. $b(x)$ is the base function, default: silu, can be set with ${\\rm base\\_fun}$\n",
    "\n",
    "2. ${\\rm scale\\_base}=1/\\sqrt{n_{\\rm in}}+e$ where $e$ is drawn from $U[-{\\rm noise\\_scale\\_base},{\\rm noise\\_scale\\_base}]$. Default: ${\\rm noise\\_scale\\_base}=0.1$.\n",
    "\n",
    "3. ${\\rm scale\\_sp}=1$\n",
    "\n",
    "4. ${\\rm spline}(x)$ is initialized by drawing coefficients independently from $N(0,({\\rm noise\\_scale}/G)^2)$ where $G$ is the grid number. Default: ${\\rm noise\\_scale}=0.1$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6459e11a",
   "metadata": {},
   "source": [
    "Default setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c3faa4ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from kan import KAN, create_dataset\n",
    "import torch\n",
    "\n",
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=0)\n",
    "x = torch.normal(0,1,size=(100,2))\n",
    "model(x) # forward is needed to collect activations for plotting\n",
    "model.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3e6d104",
   "metadata": {},
   "source": [
    "Case 1: Initialize all activation functions to be exactly linear. We need to set noise_scale_base = 0., base_fun = identity, noise_scale = 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "90d2d5de",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=0, noise_scale_base = 0., base_fun = lambda x: x, noise_scale = 0.)\n",
    "x = torch.normal(0,1,size=(100,2))\n",
    "model(x) # forward is needed to collect activations for plotting\n",
    "model.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d834a51",
   "metadata": {},
   "source": [
    "Case 2: Noisy spline initialization (not recommended, just for illustration). Set noise_scale to be a large number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "a23d4e55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=0, noise_scale=1.)\n",
    "x = torch.normal(0,1,size=(100,2))\n",
    "model(x) # forward is needed to collect activations for plotting\n",
    "model.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "37884df0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=0, noise_scale=10.)\n",
    "x = torch.normal(0,1,size=(100,2))\n",
    "model(x) # forward is needed to collect activations for plotting\n",
    "model.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4641f36a",
   "metadata": {},
   "source": [
    "Case 3: Break Symmetry. When noise_scale_base is too small, nodes are almost degenerate. Sometimes we want to break such symmetry even at initialization. For an example, please see the PDE demo, where a non-zero noise_scale_base is important for achieving fast convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8d5348a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=0, noise_scale_base=0.0)\n",
    "x = torch.normal(0,1,size=(100,2))\n",
    "model(x) # forward is needed to collect activations for plotting\n",
    "model.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a65a5a4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=0, noise_scale_base=1.0)\n",
    "x = torch.normal(0,1,size=(100,2))\n",
    "model(x) # forward is needed to collect activations for plotting\n",
    "model.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bb2b1358",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
